Saturday 7 April 2018

Swing bridge at Falkirk Wheel: rotational dynamics


I have been wondering about how much force a human can muster in a push. Mrs B reminded me that it could be done from the weight machines at the gym. I think a mere mortal might push-list 30kg. The weight lifter winner at the Commonwealth Games was nearly ten times that! Say the bridge is 4m from the pivot to the end. For a 30kg push, the torque is 300N x 4m = 1200Nm. Moment of inertia = 1/12 ML^2 for a central axis. Here L=8m. How big is M? Suppose all the wood fitted down into 8m x 0.5m x 0.5m = 2 cubic metres. Suppose the wood floats so say 900 kg per cubic metre. Mass = 1800kg. Torque = moment of inertia x angular acceleration. So angular acceleration = 0.67 rad per second per second. Suppose it reached 0.67 rad per second after 1 second and stayed at that. To do a quarter of a turn = pi/2 divided by 0.67 = 2.3 seconds. A bit low but not ridiculous. I wish I'd timed the motion but it can't have been that small. Mass must have been bigger.